Tracy Trigface

To calculate the top of a tower, Tracy Trigface measured the angle of elevation to the top of the tower from point A and found it to be15*. She then moved 30m closer to the tower, over level ground,to point B,from which the elevation to the top of the tower was 20*. Find the height of the tower,to the nearest meter.

To calculate the top of a tower, Tracy Trigface measured the angle of elevation to the top of the tower from point A and found it to be15*. She then moved 30m closer to the tower, over level ground,to point B,from which the elevation to the top of the tower was 20*. Find the height of the tower,to the nearest meter.

I can't do pictures yet.

Sketch this out. We've got points A and B defined. Call point C the base of the tower and D the top of the tower. You know angles DAB and DBC are 15 and 20 degrees, repsectively. Look at angle ADB. You can find that as well. So, in a nutshell, you can use the Law of Sines to find any unknown side of the triangle ABD.

I suggest side BD. The reason is that triangle BCD is a right triangle and we can figure out all the angles in it. So if we have the hypotenuse, we can find the side CD, right?

If you let d denote the distance between point B and the base of the tower, then the distance from point A to the tower base is d+30. Hence, h/d = tan(20), and h/(d+30) = tan(15). Solving each equation for h gives h = d[tan(20)], and h = (d+30)tan(15). Set the right-hand members of the two equations equal, and solve for d. I expect you can take it from here on your own. Hint: The tower's height, in meters, is slightly less than the freezing point of water at sea-level, in degrees, F.